EXCHANGE 


JUL    291913 


THE  INFLUENCE  OF  DENSITY  OF  GAS  ON 
THE  FORMATION  OF  CORONA 


DISSERTATION 
SUBMITTED  TO  THE  BOARD  OF  UNIVERSITY  STUDIES 

OF  THE  JOHNS  HOPKINS  UNIVERSITY 
IN  CONFORMITY  WITH  THE  REQUIREMENTS  FOR  THE 

DEGREE  OF  DOCTOR  OF  PHILOSOPHY 


By 

THEODORE  T,  FITCH 


junc, 


A  paper  to  be  presented  at  the  30th  Annual  Con- 
vention of  the  American  Institute  of  Electrical 
Engineers,  Cooperstown,  N.Y.,  June  27,  1913. 

Copyright,  1913.   By  A.I.  E.  E. 
(Subject   to  final   revision  for   the    Transactions.) 


THE  ELECTRIC  STRENGTH  OF  AIR— IV 


BY    J.    B.    WHITEHEAD    AND    T.    T.    FITCH 


I.  INTRODUCTION 

This  paper  describes  the  results  of  a  series  of  investigations 
on  the  effects  of  pressure,  temperature  and  density  of  gas  upon 
the  formation  of  the  corona  in  air.  It  is  largely  an  extension 
of  work  described  in  the  second  of  this  series  of  papers. 

The  study  of  the  influence  of  temperature  and  pressure  on 
corona- forming  voltage  was  begun  by  Ryan  in  1904.  The  in- 
fluence of  pressure  in  its  relation  to  the  size  of  conductor  was 
shown  in  the  second  of  this  series  of  papers.  The  influence  of 
temperature  and  pressure  has  been  investigated  also  by  Peek 
who  has  given  an  interesting  empirical  formula  connecting 
critical  corona  intensity  in  air  with  pressure,  temperature  and 
size  of  conductor.  The  influence  of  pressure  on  critical  corona 
intensity  has  been  studied  by  Watson  for  the  case  of  continuous 
voltage.  The  purpose  of  the  present  work  has  been  the  extension 
of  the  earlier  investigations  both  as  to  range  of  pressure  and  size 
of  conductor  and  also  to  obtain  further  information  on  the  in- 
fluence of  temperature.  Some  observations  were  also  made  with 
carbon  dioxide  as  the  gas  surrounding  the  conductor  instead  of 
air  to  see  what  part,  if  any,  is  played  by  the  density  of  the  gas. 

The  larger  part  of  the  work  is  the  study  of  variation  of  critical 
or  corona-forming  intensity  with  pressure.  For  this  work  con- 
ductors varying  from  0.438  to  0.950  cm.  in  diameter  were  used, 
and  the  pressure  was  varied  from  5  to  110  cm.  of  mercury. 

II.   REVIEW  OF  EARLIER  WORK  ON  PRESSURE  AND 

TEMPERATURE 

A  brief  review  of  earlier  investigations  on  the  variation  of 
critical  intensity  with  pressure  and  temperature  will  not  be 

1317 

266648 


131«[\  :l  WHITEHEAD  AND   FITCH:  [June  27 

out  of  place.  Some  other  points,  also,  have  such  an  intimate 
relation  to  these  variations  or  at  least  to  a  study  of  them  that 
they  will  be  mentioned. 

It  was  shown  by  Ryan1  that  for  the  one  size  of  conductor  which 
he  used  the  critical  intensity  is  a  linear  function  of  the  pressure 
from  40  to  90  cm.  of  mercury.  A  similar  relation  was  shown  to 
hold  for  variations  with  temperature  between  21  and  93  deg. 
cent. 

Watson  published  a  set  of  experiments2  in  1909  showing  a 
linear  relation  between  pressure  and  critical  intensity  for  the 
case  of  continuous  voltage.  His  range  of  pressure  was  from  36  to 
76  cm.  of  mercury  and  of  size  of  conductor  from  0.07  to  0.95 
cm.  He  also  gave  curves  showing  the  amount  of  current  passing. 

In  the  earlier  papers  of  this  series  numerous  curves  were  given 
showing  a  linear  relation  between  critical  intensity  and  pressure 
from  38  to  100  cm.  The  conductors  used  ranged  in  diameter 
from  0.122  to  0.475  cm.  Some  experiments  were  also  made 
showing  a  linear  relation  between  critical  intensity  and  temper- 
ature. Only  one  size  of  conductor  was  used.  The  range  of 
temperature  was  from  8  to  41  deg.  cent. 

It  has  further  been  shown  in  these  papers  that: 

The  critical  intensity  is  independent  of  free  ionization,  moisture 
content  and  velocity  of  the  air. 

The  visual  critical  intensity  is  identical  with  that  determined 
by  an  electroscope. 

The  critical  intensity  g  for  clean  round  conductors  for  a  pres- 
sure of  76  cm.  and  temperature  of  20  degrees  may  be  expressed 
by  the  formula: 

B 


V£ 


where  A   and  B  are  constants  and  D  is  the  diameter  of  the 
conductor.     This  formula  is  discussed  in  a  later  paragraph. 

Peek3  has  given  the  results  of  a  set  of  experiments  on  the 
variation  of  critical  intensity  with  temperature  showing  practic- 
ally a  linear  law  between  —20  and  +140  deg.  cent.  He  has 
'also  given  a  general  formula  covering  the  variations  of  critical 

1.  Ryan:     Conductivity  of  the  Atmosphere   at    High     Voltages,    TRANS. 
A.  I.  E.  E.,  Vol.  XXIII,  1904. 

2.  Electrician,  Vol.  LXIII,  1909. 

3.  Peek:     The  Law  of  Corona,  TRANS.  A.  I.  E.  E.,  Vol.  XXXI,  1912. 


1913]  ELECTRIC  STRENGTH  OF  AIR  1319 

intensity  with  change  of  temperature  and  pressure  for  a  tube 
and  concentric  conductor  as  follows: 


where  g  is  the  critical  intensity  in  kilo  volts  per  cm.,  r  is  the  radius 
of  conductor  and 


273  +  t 

p  being  the  pressure  in  cm.  of  mercury  and  /  the  temperature 
centigrade.  So  far  as  we  can  find  the  only  statements  he  has 
given  concerning  the  influence  of  pressure  on  the  variation  of 
critical  intensity  are  a  curve4  giving  observations  on  a2.54-cm. 
conductor  for  pressures  from  2  to  65  cm.  and  a  table  of  values 
of  d  and  corresponding  values  of  g  in  closing  the  discussion  of  his 
1912  paper.5  No  description  of  his  methods  was  given. 

Ill  .   PRESENT  WORK 

The  observations  which  are  recorded  in  this  paper  were  made 
in  the  spring  of  1912.  They  aim  to  supply,  in  part,  the  lack  of 
sufficiently  extensive  data  on  variation  of  critical  corona  inten- 
sity with  pressure  and  size  of  conductor. 

Apparatus  and  Equipment.  For  the  pressure  measurements  a 
20-cm.  iron  tube  about  90  cm.  in  length  was  used.  The  ends 
were  fitted  with  insulating  caps  about  18  cm.  long.  These 
caps  were  made  of  impregnated  fibre,  and  served  the  double 
purpose  of  insulation  and  sealing  for  the  variation  of  air  pressure 
both  above  and  below  that  of  the  atmosphere.  A  rotary  air 
pump  permitted  evacuation  of  the  tube  to  about  five  cm.  of 
mercury  in  five  minutes.  Most  changes  of  pressure  could  be 
made  in  a  minute  or  two,  but  owing  to  numerous  joints  necessary 
for  insulation  purposes  there  was  present  some  leakage,  which 
necessitated  a  longer  time  to  exhaust  to  the  lowest  pressure 
reached,  and  set  the  limit  of  about  five  cm.  as  the  minimum. 

A  small  glass  window  was  placed  in  the  tube  for  making 
visual  observations  of  the  corona,  but  during  most  of  the  work 
the  gold  leaf  electroscope  was  used  for  detecting  the  point  at 

4.  Peek:     "  Nature  of  Corona,"  Gen.  Elec.  Review,  December,  1912. 

5.  Peek:    PROC.  A.  I.  E.  E.f  November,  1912. 


320 


WHITEHEAD  AND   FITCH: 


[June  27 


T  «ORONA  TUBE 

W  CHARGED  WIRE 

F  GOLD  LEAF 

CT  ELECTROSCOPE  CASE 

I  SULPHUR  INSULATOR 

R  CONCENTRIC  CONDUCTOR 

O  WINDdW 


which  corona  begins.    This  method  has  been  described  in  detail 

in  the  first  of  these  papers  so  no  further  description  is  necessary 

here.     Fig.  1  shows  the  general  arrangement  of  the  apparatus. 

The    beginning    of    corona    is 

very  sharply  defined.  A  change 

of  one  per  cent  or  less  in  the 

voltage  will  cause  the  time  of 

complete  discharge  to  change 

from    about    a    half    hour    to 

five   seconds.     Any    difference 

between      the      beginning     of 

corona  as  observed  by  the  eye 

and  by   the   discharge   of   the 

electroscope  is  within  this  small 

error  of  observation. 

The  observations  on  the  in- 
fluence of  temperature  were 
made  with  a  similar  apparatus, 
except  that  the  tube  was  in 
this  case  surrounded  by  a 
water  jacket.  Hand  stirring 
of  the  water  was  found  to  be 
sufficient  to  keep  the  tempera- 
ture of  the  air  within  the  tube 
uniform  to  about  two  degrees. 
Only  the  smaller  sizes  of  con- 
ductor could  be  used  in  this 
apparatus  owing  to  spark-over 
troubles  occasioned  by  the 
reduced  size  of  outer  tube. 
The  heating  was  done  by  gas 
burners  and  ice  was  used  for 
getting  reduced  temperature. 

Source  of  Power.  The  power 
for  all  the  experiments  was 
drawn  from  a  10-kw.,  100,000- 
volt  transformer.  The  trans- 
former was  operated  by  a 
motor-generator  set  of  7 . 5  kw. 

capacity,  the  generator  field  being  excited  by  a  storage  battery, 
resulting  in  good  voltage  control.  All  experiments  were  made  at 
a  frequency  of  60  cycles.  The  transformer  is  provided  with  a 


FIG. 


1 .  — ARRANGEMENT 
APPARATUS 


OF 


1913] 


ELECTRIC  STRENGTH  OF  AIR 


1321 


test  coil  giving  120  volts  for  100,000  volts  on  the  high-tension 
terminals  as  computed  from  the  ratio  of  primary  and  secondary 
turns.  This  test  coil  was  used  entirely  in  making  measurements 
of  the  voltage.  All  determinations  of  ratio  of  maximum  to  mean 
effective  voltage  were  also  obtained  from  this  coil. 

Ratio  of  Maximum  to  Mean  Effective  Voltage.  For  the  purpose 
of  checking  the  results  this  ratio  was  determined  by  two  methods. 
The  first  makes  use  of  the  oscillograph,  the  second  of  a  rotating 
contactor  and  the  principle  of  the  potentiometer. 

The  ratio  was  determined  from  the  oscillograms  by  reading  a 
number  of  ordinates,  usually  about  30  or  40  to  a  cycle.  From 

these  ordinates  taken  at  equal 
distances  the  ratio  of  maximum 
to  the  square  root  of  the  mean 
square  value  was  computed. 
The  principal  difficulty  with 
this  method  is  to  obtain  an 
oscillogram  with  lines  suffi- 
ciently sharp  and  narrow. 

The  contactor  method  is  in- 
dicated in  Fig.  2,  the  contact 
wheel  being  placed  on  the 
generator  shaft.  In  the  actual 
apparatus  a  handle  was  pro- 
vided for  readily  shifting  the 
point  of  contact.  By  reference 
to  the  galvanometer  the  con- 
tact can  be  shifted  until  the 
closure  occurs  on  the  peak  of 
the  wave.  Then  the  slider 
on  the  rheostat  is  moved  until  the  galvanometer  indicates  zero 
deflection.  The  readings  of  the  continuous  and  alternating 
voltmeters  are  then  taken.  The  ratio  of  their  readings  in  volts 
is  the  ratio  desired,  the  direct-current  voltmeter  indicating  the 
maximum  voltage  and  the  alternating-current  voltmeter  the 
mean  effective  value. 

The  chief  difficulty  with  this  method  is  to  keep  the  source 
of  alternating  voltage  sufficiently  steady  during  the  time  neces- 
sary for  an  observation.  A  damped  galvanometer  of  fairly 
high  sensibility  is  required.  Only  the  relative  calibration  of  the 
voltmeters  is  necessary  since  the  ratio  is  all  that  is  required. 
The  alternating  voltmeter  used  was  of  the  electrodynamometer 


FIG.  2. — METHOD  OF  MEASURING 
RATIO  OF  MAXIMUM  TO  MEAN- 
EFFECTIVE  VOLTAGE 


1322 


WHITEHEAD  AND   FITCH: 


[June  27 


type  and  it  was  compared  with  the  direct-current  voltmeter  by 
taking  the  mean  of  readings  with  reversed  polarity. 

Table  I,  of  which  Fig.  3  is  a  plot,  gives  the  ratio  of  maximum 
to  mean  effective  voltage  for  the  various  voltages  on  the  test 


gji.bo 

_j 

o 

o 

^1.20 


°  POINTS  BY  OSCILLOGRAPH 
11         l(    CONTACTOR 


10 


20       30       40       50       60       70 

VOLTS  ON  TEST  COIL 


80 


FIG.  3. — RATIO    OF    MAXIMUM    TO    MEAN    EFFECTIVE    VOLTS. 
TEST  COIL  OF  100,000- VOLT  TRANSFORMER 


FROM 


coil  of  the  transformer  used  in  the  experiments.  The  values 
taken  from  the  curve  were  used  in  making  reductions  of  readings 
on  critical  intensity. 

Fig.  4  is  a  reproduction  from  a  typical  oscillogram. 


TABLE  I 


Max. 

T?  o-f  i/-\           — 

Test  coil  volts 

rcatio  — 

Mean  en. 

Contactor 

Oscillograph 

From  curve 

4 

1.395 

1.400 

7 

1.420 

1.420 

10 

1.450 

.440 

15 

1.431 

.440 

20 

1.459 

.445 

25 

1.436 

.445 

30 

1.429 

.445 

35 

1.438 

.445 

50 

1.444 

1.446 

.440 

60 

1.421 

1.430 

.440 

75 

1.452 

1.427 

.440 

1913] 


ELECTRIC  STRENGTH  OF  AIR 


1323 


Variation  of  Critical  Intensity  with  Gas  Pressure.  Fig.  5  shows 
the  observed  variation  of  critical  corona  voltage  with  pressure, 
while  Fig.  6  shows  the  corresponding  variation  of  critical  inten- 
sity computed  from  the  same  observations.  As  mentioned  before, 
nine  conductors  varying  from  0.238  to  0.950  cm.  in  diameter 
were  used.  Above  30  or  40  cm.  pressure  the  curves  are  nearly 
straight;  the  curvature  being  so  slight  as  to  be  within  the  error 
of  observation.  They  explain,  therefore,  the  conclusion  of  the 
earlier  paper  that  the  relation  between  pressure  and  critical 
intensity  is  linear  in  this  region. 


FIG.  4  — TAKEN  AT  60  CYCLES  AND  60  VOLTS 


We  have  used  the  expression 


dv 


dr 


for  calculating  the  critical  intensity  in  kilo  volts  per  cm.  from 
the  observed  critical  voltage  on  the  transformer  test  coil.  E  is 
the  maximum  voltage  on  the  conductor  obtained  by  taking  into 
account  the  ratio  of  transformation  of  the  transformer,  and  the 
ratio  of  maximum  to  mean  effective  voltage,  while  r  and  R 
are  the  radii  of  conductor  and  tube,  respectively. 

Table  II  gives  a  typical  set  of  observations. 

Several  readings  were  taken  at  each  pressure  as  shown  in  the 
readings  for  the  last  three  pressures.  The  pressure  was  deter- 
mined by  use  of  a  gauge  or  monometer.  This  method  gives,  of 
course,  only  the  difference  of  pressure  between  that  in  the  tube 


1324 


WHITEHEAD  AND   FITCH: 


[June  27 


0        10       20 


40        50       60        70       SO       90      100     110 
PRESSURE  IN  CM.  OF  HG. 


pIG    5  — OBSERVED   VARIATION   OF   CRITICAL   CORONA   VOLTAGE   WITH 
PRESSURE.    TRANSFORMER  RATIO  =  833 


lo      "u     ao     -to      no     oo      ro     80     90     100 

D-^r^Qiipc    IN'   CM.   OF    HG. 

FIG.  6  — VARIATION  OF  CRITICAL  INTENSITY  WITH  PRESSURE  AND  SIZE 
OF  CONDUCTOR  AT  20  DEC.  CENT. 


1913] 


ELECTRIC  STRENGTH  OF  AIR 


1325 


and  atmospheric.  For  this  reason  it  was  necessary  to  read  the 
barometer  to  obtain  the  absolute  pressure.  The  voltage  was  read 
by  two  Weston  alternating-current  voltmeters  of  suitable  ranges 
connected  to  the  test  coil  of  the  transformer,  as  stated. 
In  taking  readings  the  electroscope  was  first  charged  and 
then  the  voltage  gradually  raised  till  the  electroscope  was 
suddenly  discharged,  as  shown  by  the  fall  of  the  gold  leaf.  Atten- 


Diameter  of  conductor  0.316  cm. 


TABLE  II 
Transformer  ratio  833 


r  log  R/r 


1.539 


Gauge  read- 
ings 
mm.  of  hg. 

Diff. 

Temp, 
deg.  cent 

Baro- 
meter 

Pres- 
sure 
mm. 

Test 
coils 
volts 

Ratio 
max. 

Critical 
kilo- 
volts 
max. 

Critical 
inten- 
sity 
kv.  cm. 

eff. 

288 

1000 

712 

18.2 

760 

48 

4.5 

1.40 

5.2 

8.0 

316 

960 

644 

18.2 

760 

116 

7.2 

1.42 

8.5 

13.1 

348 

915 

567 

18.2 

760 

193 

10.3 

1.44 

12.3 

18.9 

361 

910 

549 

19.8 

756 

207 

10.9 

1.44 

13.0 

20.0 

365 

909 

544 

19.8 

756 

212 

11.2 

1.44 

13.4 

20.6 

431 

846 

415 

19.8 

756 

341 

15.7 

1.44 

18.9 

29.1 

484 

799 

315 

19.8 

756 

441 

19.3 

1.44 

23.2 

35.7 

530 

750 

220 

19.8 

756 

536 

22.4 

1.445 

27.0 

41.5 

592 

710 

118 

19.8 

756 

638 

25.5 

1.445 

30.7 

47.2 

756 

29.3 

1.445 

19.8 

756 

756 

29.5 

1.445 

35.5 

54.6 

756- 

29.5 

756 

29.3 

755 

597 

158 

914 

34.0 

1.445 

755 

597 

158 

914 

33.9 

754 

597 

157 

19.8 

756 

913 

34.0 

41.0 

63.1 

754 

597 

157 

913 

33.9 

849 

554 

295 

1051 

38.2 

850 

555 

295 

19.8 

756 

1051 

38.2 

. 

1.445 

46.0 

70.8 

850 

555 

295 

1051 

38.2 

850 

555 

295 

1051 

38.2 

tion  is  called  to  the  accuracy  with  which  observations  may  be 
repeated. 

Empirical  Formulas.     As  stated  before,  Peek  has  given  the 
formula 


connecting  the  critical  intensity  g  in  kilo  volts  per  cm.   with 
pressure,  temperature  and  radius  of  conductor.     Fig.  8  shows 


1326 


WHITEHEAD  AND   FITCH: 


[June  27 


curves  for  three  sizes  of  conductor  for  the  temperature  20  deg. 
cent.  As  indicated,  the  circles  are  observed  points  while  the 
full  lines  are  plotted  from  the  formula  given  above.  It  is  seen 
that  as  the  formula  stands  it  does  not  meet  our  observations 
very  closely,  though  it  gives  a  curve  of  the  correct  general  form. 
By  suitable  changes  in  the  constants  the  formula  is  brought 
into  close  agreement. 
*  Fig.  9  is  plotted  from  the  formula 


33.65 


(l+   °» 
V  VSr  I 


(2) 


The  circles  show  the  observed  points  as  before.    It  is  seen  that 
with  the  formula  so  changed  it  represents  the  observations  about 


3         45         0         7          8          9 
DIAMETER  OF  CONDUCTOR  MM. 


10 


FIG.  7. — VARIATION  OF  CRITICAL  INTENSITY  WITH  SIZE  OF  CONDUCTOR 
AT  20  DEG.  CENT.  AND  76  CMJ  PRESSURE 

as  closely  as  the  readings  can  be  taken.  This  formula  gives  zero 
voltage  for  zero  pressure  provided  r  has  a  value  greater  than  zero, 
which,  of  course,  it  has  for  any  real  case.  As  the  present  observa- 
tions run  only  as  low  as  4  or  5  cm.  pressure,  they  furnish  no  test 
on  this  point.  Investigations  are  now  under  way  to  determine 
what  becomes  of  the  corona  at  very  low  pressures. 

If  in  equation  (2)  the  value  of  d  at  76  cm.  pressure  and  tempera- 
ture 20  deg.  be  substituted,  the  following  formula  is  obtained: 


g  =  34  + 


11.2 

VD 


(3) 


This  formula  gives  the  variation  of  critical  intensity  with  D 
the  diameter  of  conductor  at  standard  temperature  and  pressure. 


1913] 


ELECTRIC  STRENGTH  OF  AIR 


1327 


The  curve  in  Fig.  7  is  a  plot  from  this  equation  while  the  circles 
are  observed  points.  In  the  earlier  work  a  formula  of  the  same 
form  but  with  different  constants  was  given,  namely: 


FROM  FEEK'fa  EQUATION 

:/..  >  315(1  + 

00 00  OBSERVED  POINTS. 


10       20       30       40       50       60       70       80       90      100 

PRESSURE  IN  CM.  OF  HG. 
FIG.  8 


10       20        30       40       50       60       70       80       90      1UU 

PRESSURE  IN  CM.  OF  HG. 
FIG.  9 

The  first  constant  of  formula  (4)  is  less  than  that  of  formula 
(3)  while  the  second  is  greater,  so  the  difference  is  largely  one 
of  curvature.  What  difference  there  is  over  the  range  of  con- 
ductors observed  is  accounted  for  by  a  small  discrepancy  in  the 
ratios  of  transformation  of  the  transformers  used  in  the  earlier 


1328 


WHITEHEAD  AND   FITCH: 


[June  27 


GO 


;30 


experiments  and  in  the  present  ones.  It  was  found  by  trial  in  the 
earlier  experiments  that  the  indicated  critical  voltage  with  the 
30, 000- volt  transformer  with  which  those  experiments  were 
conducted  was  54  kv.  for  a  0.345-cm.  conductor  and  52.4  for 
the  100,000-volt  transformer 
which  was  used  in  the  present 
set  of  experiments.  These 
two  differing  values  were  ob- 
tained at  the  same  time  and  o 
with  voltage  from  the  same  340 
generator.  Allowing  for  this  ^ 
discrepancy  the  present  ob-  £j 
servations  are  brought  into  ^20 
close  agreement  with  the  older 
values.  As  the  purpose  of 
this  work  is  the  investiga- 
tion of  the  influence  of  density 
of  gas  on  critical  corona  in- 
tensity, and  as  the  above 
discrepancy  does  not  affect 
the  results  relatively,  its  elimination  has  been  left  to  a  later  date. 
Variation  of  Critical  Intensity  with  Temperature.  The  curves 
of  Fig.  10  show  the  variation  of  critical  corona  voltage  with 
temperature  corrected  to  the  pressure  76  cm.  Table  III  gives 
the  data  from  which  the  curves  were  plotted.  The  values  com- 
puted are  from  the  formula 


10 


OBSERVED  POINTS 
•COMPUTED  FROM  EQUATION 
0  =  33.65(1  +  ^-) 


5  10       20       30      40        50       60 

y    TEMPERATURE  DEGREES  CENTIGRADE 

FIG.  10. — VARIATION  OF  CRITICAL 
INTENSITY  WITH  TEMPERATURE. 
AT  76  CM.  PRESSURE 


TABLE  III 


Test  coil  volts 

Critical  intensity 

Diameter  of 

Temp. 

conductor 

deg.  cent. 

Barometer 

Read 

Corrected 

Obs. 

Comp. 

0.238 

4.0 

758 

22.6 

22.6 

60.3 

59.8 

24.3 

760 

21.5 

21.5 

57.5 

56.6 

55.4 

754 

19.8 

20.0 

53.5 

52.3 

0.315 

3.7 

758 

26.4 

26.4 

57.6 

56.8 

24.2 

760 

25.0 

25.0 

54.3 

53.4 

50.8 

754 

23.1 

23.3 

50.7 

50.0 

0.399 

6.3 

758 

29.1 

29.1 

53.7 

54.2 

24.2 

760 

28.1 

28.1 

51.8 

51.3 

51.0 

754 

25.9 

26.1 

48.1 

47.8 

1913] 


ELECTRIC  STRENGTH  OF  AIR 


1329 


The  diameter  of  tube  used  as  outer  conductor  in  these  experi- 
ments was  10 .5  cm.  Trie  curves  in  Fig.  9  are  practically  straight 
lines  as  the  range  of  temperature  is  not  great  enough  to  bring 
out  any  curvature.  The  agreement  with  the  revised  Peek 
equation  is  also  very  close  here. 

Influence  of  Density  of  the  Medium  on  Critical  Intensity.  A 
simple  calculation  from  the  gas  equation 

pv  =  R  T 

shows  that  the  pressure  coefficient  and  temperature  coefficient 
interpreted  in  terms  of  the  change  in  volume  of  unit  mass  of 
gas  are  the  same.  In  other  words  the  critical  corona  intensity 
in  air  varies  nearly  as  the  density  whether  such  change  is  pro- 
duced by  a  change  of  pressure  or  temperature.  This  idea  is 
implicitly  stated  in  Peek's  equation  in  his  density  factor.  It 
must  be  remembered,  however,  that  his  definition  gives  only 


40 


o 
>30 


20 

£ 

-J  10 


FCINTS  TAKEN  IN  AIR 


.316  CM. DIAMETER 


10 


40       50      60       70       bO       90      100 

PRESSURE  IN  CM.  OF  HG. 


20        30 

\-/ 

FIG.  11. — EFFECT  OF  DENSITY  OF  THE  MEDIUM  ON  CRITICAL  INTENSITY 


the  relative  density.  With  a  view  to  the  more  definite  investiga- 
tion of  the  influence  of  density  as  the  mass  per  unit  volume  we 
have  made  some  interesting  preliminary  observations  on  the 
corona  in  a  gas  heavier  than  air. 

In  Fig.  11  are  shown  two  curves  of  the  variation  of  critical 
intensity  with  pressure,  one  in  air  and  the  other  in  a  mixture 
of  carbon  dioxide  and  air,  but  containing  about  90  per  cent  by 
volume  of  the  former.  Owing  to  leakage  of  the  tube  it  was  not 
possible  to  fill  it  with  the  pure  gas.  It  is  seen  that  there  is  little 
change  due  to  the  presence  of  the  carbon  dioxide  although  its 
density  is  about  1 . 5  times  that  of  air.  It  appears  then  from  these 
experiments  that  the  variation  of  critical  intensity  does  not,  in 
fact,  depend  on  the  density,  but  is  rather  a  function  of  the  separa- 
tion of  the  molecules  of  the  gas,  since  according  to  the  law  of 
Avogadro  the  number  of  molecules  in  a  given  volume  or  gas  is  a 


1330 


WHITEHEAD  AND   FITCH: 


[June  27 


function  of  the  pressure  and  temperature  only,  and  does  not 
depend  on  the  nature  of  the  substance.  The  indication  from 
these  curves  then  is  that  the  relation  of  the  electric  intensity  and 
corona  formation  is  found  in  the  average  separation  of  the 
molecules.  This  is  in  fact  a  principle  tenet  of  the  theory  of 
secondary  ionization  or  ionization  by  collision  as  explaining  all 
forms  of  spark  discharge  in  gases.  The  opinion  has  been  expressed 
in  several  places  in  this  series  of  papers  that  the  theory  of  second- 


4         0         8        10       12        14       16 

AIR  PRESSURE    ATMOSPHERES 


FIG.   12. — SPARKING    POTENTIALS    BETWEEN    SPHERES,     BY    WATSON 

ary  ionization  offers  the  most  promising  explanation  of  corona 
formation. 


IV.   COMPARISON    WITH    RESULTS    ON    SPARKING    POTENTIALS 
Fig.   12  is  reproduced  from  a  paper  by  Watson  on  "  The 
Dielectric  Strength  of  Air."6    The  curves  show  the  variation  of 
the  sparking  potentials  between  spheres  with  variation  of  pres- 
sure.    The  pressures  range  from  atmospheric  upward  so  that 
,6.    Jour.  InsL  Elec.  Engrs.,  Vol.  XLIII,  1909. 


1913]  ELECTRIC  STRENGTH  OF  AIR  1331 

they  are  not  directly  comparable  with  the  pressures  in  the  present 
set  of  corona  experiments.  From  the  work  of  other  observers, 
however,  it  is  known  that  the  curves  extend  down  toward  the 
zero  until  they  reach  the  so-called  "  critical  pressure."  Upon 
further  reduction  of  pressure  the  curves  turn  sharply  upward. 
These  critical  pressures  vary  with  the  length  of  spark  gap,  ranging 
from  3  to  0.3  mm.  for  spark  gaps  of  1  to  10  mm.,  respectively.7 

It  is  seen  by  reference  to  the  curves  that  their  general  shape 
is  the  same  as  for  critical  corona  intensity.  The  chief  question 
of  interest  in  both  cases  is  the  departure  from  the  linear  law  as 
the  curvature  is  probably  due  to  a  common  cause.  By  analogy 
with  curves  for  sparking  potentials  it  may  be  anticipated  that 
the  critical  corona  intensity  may  rise  at  very  low  pressures.  It 
is  well  known  that  it  is  difficult  to  get  the  vacuum  tube  discharge 
at  very  high  vacua. 

The  results  obtained  with  corona  in  carbon  dioxide  were  to  be 
anticipated  from  Paschen's  law.  This  law  states  that  the  spark- 
ing potential  depends  on  the  product  of  the  pressure  and  the 
spark  length.  Curves  plotted  with  products  of  pressure  and 
spark  length  as  abscissas  and  sparking  potentials  as  ordinates 
are  nearly  the  same  for  air  and  carbon  dioxide  but  differ  con- 
siderably for  hydrogen.  No  attempt  was  made  to  try  hydrogen 
as  the  medium  surrounding  the  conductor  in  the  present  set  of 
experiments  owing  to  the  presence  of  some  leakage  of  the  tube 
which  might  have  resulted  in  the  production  of  an  explosive 
mixture.  We  wish  to  emphasize  the  simplicity  of  the  corona 
apparatus  as  a  method  for  studying  the  theory  of  gaseous  con- 
duction. 

V.   DISCUSSION 

As  most  of  the  observed  laws  of  corona  formation  are  in  accord 
with  the  theory  of  ionization  by  collision,  a  brief  statement  of 
some  of  the  fundamental  experiments  and  conclusions  of  that 
theory  will  not  be  out  of  place. 

When  two  parallel  conducting  plates  are  connected  to  a  source 
of  potential  difference  and  the  gas  between  them  ionized  by  X- 
rays  or  radium,  it  is  found  that  a  current  passes.  This  current 
increases  at  first  as  the  potential  difference  is  increased,  but  later 
attains  a  stationary  value.  No  further  increase  of  the  current 
with  increasing  voltage  is  noted  until  a  considerably  higher  volt- 
age is  reached  when  the  current  again  increases  rapidly  with  in- 
creasing voltage.  The  interpretation  of  this  phenomenon  is 

7.    "  Conduction  of  Elec.  Through  Gases,"  J.  J.  Thomson,  1906. 


1332  WHITEHEAD  AND   FITCH:  [June  27 

that  the  X-rays  produce  ions  at  a  definite  rate  so  that  the 
current  which  can  be  produced  by  sweeping  out  all  these  ions 
has  a  limit.  The  stationary  value  of  the  current  spoken  of, 
marks  this  limit.  When,  however,  the  voltage  becomes  suffi- 
ciently high  the  ions  attain  a  velocity  which  enables  them  to 
produce  new  ones  by  collision  with  neutral  atoms.  This  is 
known  as  ionization  by  collision  or  secondary  ionization.  This 
theory  of  ionization  by  collision  accounts  for  the  order  of  mag- 
nitude of  the  critical  corona  voltage  which  in  the  limiting  case  of 
plane  surfaces  is  approximately  30  kv.  per  cm.  The  mean  free 
path  of  the  electrons  is  about  6  X  10~5  cm.  at  76  cm.  pressure 
and  20  deg.  cent,  as  has  been  shown  by  Townsend  and  others. 
This  is  about  six  times  the  mean  free  path  of  the  molecules  of  the 
gas.  For  the  ordinary  sizes  of  conductors  the  voltage  over  a 
mean  free  path  of  an  electron  is  about  2  volts.  This  indicates 
that  the  critical  intensity  is  that  which  gives  the  ionizing  voltage 
of  about  10  volts8  in  a  distance  of  five  times  the  mean  free  path, 
or  in  other  words  some  of  the  electrons  having  a  free  path  of 
five  or  more  times  the  average,  start  the  corona. 

The  ionization  theory  fails  as  yet  to  show  why  the  critical 
intensity  varies  with  the  size  of  conductor  and  why  the  variation 
of  critical  intensity  with  pressure  does  not  follow  a  linear  law. 
As  has  been  frequently  shown,  the  critical  intensity  rises  quite 
rapidly  as  the  size  of  conductor  is  reduced.  The  intensity  in  the 
gas  falls  away  as  l/r  where  r  is  the  distance  from  the  center  of 
the  conductor,  and  from  this  it  is  seen  that  the  intensity  dimin- 
ishes much  more  rapidly  in  the  immediate  neighborhood  of  a 
small  conductor  than  a  large  one.  Nevertheless,  the  diminution 
in  a  distance  of  five  or  ten  mean  free  paths  of  an  electron  is 
negligibly  small  in  any  practical  case. 

The  corona  begins  and  ends  at  approximately  the  same  voltage 
on  the  e.m.f .  wave.  This  indicates  that  the  rate  of  recombination 
of  the  ions  is  very  great.  It  appears  possible  from  this  fact  that 
the  corona  will  not  start  until  the  intensity  is  high  enough  over 
some  depth  such  as  half  a  mm.  on  account  of  the  great  amount 
of  recombination  which  goes  on  in  the  neighboring  space,  where 
the  intensity  is  too  low. 

VI.   CONCLUSIONS 

1 .   The  critical  corona-forming  electric  intensity  in  air   has 
been  determined  over  the  range  of  pressure  from  5  cm.  to  108  cm. 
8.    Bishop:    Physical  Review,  Vol.  XXXIII,  1911. 


1913]  ELECTRIC  STRENGTH  OF  AIR  1333 

of  mercury,  for  nine  sizes  of  round  conductor  of  diameters  from 
0.23  to  0.95  cm. 

2 .  A  few  observations  on  the  influence  of  temperature  within 
the  range  of  5  deg.  to  55  deg.  cent,  are  also  recorded. 

3 .  The  results  are  in  substantial  agreement  with  the  empirical 
relation  between  electric  intensity,   pressure   and   temperature 
suggested  by  Peek. 

4 .  Experiments  with  carbon  dioxide  indicate  that  the  critical 
corona  intensity  is  independent  of  the  absolute  density  of  the  gas, 
but  depends  on  the  number  and  spacing  of  the  molecules,  in 
accord  with  the  theory  of  secondary  ionization. 

BIBLIOGRAPHY 

Steinmetz:    Dielectric  Strength  of  Air,  TRANS.  A.  I.  E.  E.,  Vol.  XV,  1898 

Scott:    High  Voltage  Power  Transmission,  TRANS.  A.  I.  E.  E.,  Vol.  XV, 
1898. 

Ryan:    Conductivity  of  Atmosphere  at  High  Voltages,  TRANS.  A.  I.  E.  E., 
Vol.  XXIII,  1904. 

Mershon:    High  Voltage  Measurements  at  Niagara,  TRANS.  A.  I.  E.  E., 
Vol.  XXVII,  1908. 

Balch:     "  80,000- Volt  Transmission  Line,"  Jour,  of  Elec.,  1904. 

Brecht:     "A  500,000- Volt  Experimental  Line,"  Electrotechn.  Anzeiger, 
Vol.  XXVI,  1909. 

Lyndon:     "  The  Corona  and   Design  of  High  Tension   Lines,"   Elec. 
Review  and  Western  Electn.,  Vol.  LIV.   1909. 

Watson:    "  Atmospheric  Loss  under  Continuous  Current,"  Electrician, 
September  3,  1909;    February  11,  18,  1910. 

"  Dielectric  Strength  of  Compressed  Air,"  Jour.  Inst.  Elec.  Engr., 
Vol.  XLIII,  1909. 

Moody  and  Faccioli:     Experiments  on  Corona,  TRANS.  A.  I.  E.  E.,  Vol. 
XXVIII,  1909. 

Kemp  and  Stephens:     "  Disruptive  Voltage  in  Air,"  Inst.  Elec.  Engr., 
Vol.  XLIV,  1910. 

Hayden  and  Steinmetz:    Disruptive  Strength  of  Air,  TRANS.  A.  I.  E.  E., 
Vol.  XXIX,  1910. 

Whitehead:     The  Electric  Strength  oj  Air,  I,  II,  III,  TRANS.  A.  I.  E.  E., 
1910,   19J1,   1912. 

Peek:     The  Law  of  Corona  and  the  Dielectric  Strength  of  Air,  I  and  II, 
TRANS.  A.  I.  E.  E.,  1911,  1912. 

"  The  Nature  of  Corona,"  G.  E.  Renew,  December,  1912. 
Gorges,  Weidig  and  Jaensch:     "  Experiments  on  Corona  Loss,"  Electro- 
techn. Zeitschr.,  32,  1911. 

Wecker:    "  Sparking  Pressure  under  Commercial  Conditions,"  Zeitschr. 
Verins.  Deutsch.  Eng.,  55,  1911. 

West:  High  Voltage  Line  Loss  Tests,  TRANS.  A.I.E.E.,  Vol  XXX,  1911. 

Faccioli:   Tests  of  Losses  on  High  Tens-ion  Lines,  TRANS.  A.  I.  E.  E.,  1911 . 

Zickler:   "  Zur   Berechnung   der    Koronaverluste,"     Electrotechn.    u-nd 
Maschinenbau,  September  15,  1912. 


BIOGRAPHICAL  NOTE 

Theodore  Thornbur  Fitch,  son  of  Henry  H.,  and  Elizabeth 
Fitch  was  born  in  Sac  County,  Iowa,  September  23,  1879.  In 
1898  he  graduated  from  Sac  City  Institute,  a  college  prepara- 
tory school.  He  spent  the  year  of  1899-00  at  the  State  Univer- 
sity of  Iowa,  and  the  following  scholastic  year  entered  Iowa 
State  College  where  he  graduated  in  the  course  in  Civil  Engineer- 
ing in  1903.  He  spent  the  year  following  in  the  U.  S.  Coast  and 
Geodetic  Survey.  The  following  year,  1904-1905  he  took  up  the 
study  of  Electrical  Engineering  at  Iowa  State  College.  Since 
1906  he  has  been  continuously  on  the  staff  of  the  Bureau  of 
Standards  at  Washington,  D.  d,  being  now  an  Assistant  Physi- 
cist. In  1910  he  took  up  graduate  work  at  Johns  Hopkins  Uni- 
versity choosing  Physics  as  principal  subject  and.  Mathematics 
and  Astronomy  as  subordinate  subjects.  He  took  lectures  under 
Professors  Ames  and  Whitehead  and  Drs.  Anderson,  Cohen  and 
Pfund.  He  also  took  a  number  of  lecture  courses  given  at  the 
Bureau  of  Standards  by  Drs.  A  i,  Pfund  and  Buckingham- 


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